Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 476: 89

Answer

$\log{2} +3\log{x} -2\log{y}$

Work Step by Step

Recall: (1) Product Property of Logarithms: $\log_a{b}+\log_a{c}=\log_a{bc}$. (2) Power Property of Logarithms: $\log_a{b^n} = n\cdot \log_a{b}$ Use the Product Property to obtain: \begin{align*} &=\log{2x^3} + \log{y^{-2}}\\ \end{align*} Use the Power Property to obtain: \begin{align*} \log{2} + \log{x^3} + \log{y^{-2}}&=\log{2} +3\log{x} +(-2\log{y})\\ &=\log{2} +3\log{x} -2\log{y} \end{align*}
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